Is Liquidity Related to Prediction Market Efficiency?

Paul C. Tetlock*

December 2007

Abstract

I investigate the relationship between liquidity and market efficiency using data from

short-horizon binary outcome securities listed on the TradeSports exchange. I find that

liquidity does not reduce—and sometimes increases—deviations of prices from financial

and sporting event outcomes. One explanation is that limit order traders are naïve about

other traders’ knowledge and unwittingly bet against them, which can slow the response

of prices to information. Consistent with this explanation, the limit orders that execute

during informative events have negative expected returns; and limit orders often execute

against traders who exploit the well-known favorite-longshot bias in prices.

* Please send all comments to paul.tetlock@yale.edu. I am currently visiting the finance department at

Yale, on leave from Texas. I am extremely grateful to TradeSports for their cooperation in allowing me to

collect the liquidity data, and their generosity in providing additional trading data. I thank Yakov Amihud,

Malcolm Baker, Ed Glaeser, Larry Glosten, John Griffin, Robert Hahn, Bing Han, Alok Kumar, Terry

Murray, Chris Parsons, Matt Spiegel, Laura Starks, Avanidhar Subrahmanyam, Sheridan Titman, Justin

Wolfers, Eric Zitzewitz, and seminar participants at Kansas and Texas for helpful comments.

1

I. Introduction

There is a growing body of theoretical and empirical research on securities

markets for contingent claims on uncertain events, often called prediction or information

markets. A key finding in this literature is that the prices in prediction markets can help to

produce forecasts of event outcomes with a lower mean squared prediction error than

conventional forecasting methods. For example, incorporating the prices in prediction

markets increases the accuracy of poll-based forecasts of election outcomes (Berg,

Forsythe, Nelson and Rietz (2003)), official corporate experts’ forecasts of printer sales

(Chen and Plott (2002)), and statistical weather forecasts used by the National Weather

Service (Roll (1984)).1

This study provides new evidence on how the forecasting accuracy of event

prediction markets depends on market liquidity. I use three years of intraday data on

one-day binary outcome securities based on sports and financial events traded on an

online exchange, TradeSports.com. I use three standard measures of securities liquidity,

low quoted bid-ask spreads, high market depth, and high trading volume. The idea is that,

in a liquid market, traders can cheaply buy and sell large quantities—e.g., O’Hara (1995).

I measure event forecasting accuracy as the difference between securities prices

and terminal cash flows. Unlike securities in conventional financial markets, I study

TradeSports’ securities that pay a single terminal cash flow at the end of their one-day

horizons, allowing me to repeatedly observe securities’ fundamentals (Thaler and Ziemba

(1988)). In addition, many of the securities are exposed to negligible systematic risks.

1 See Wolfers and Zitzewitz (2004) for a survey of the literature on prediction markets.

2

Thus, I can directly measure absolute pricing efficiency as the deviation of prices from

terminal cash flows.

I find that liquidity does not reduce—and sometimes increases—deviations of

securities prices from financial and sporting event outcomes. Prices can deviate from

outcomes because average prices differ from average event outcomes (i.e., poor

calibration), or because prices do not distinguish between events with different

probabilities (i.e., poor resolution). I find that the prices of liquid securities are not better

calibrated, and actually exhibit poorer resolution than the prices of illiquid securities.

These results are important for both direct and indirect reasons. Directly, the

findings address a key concern in using prediction markets prices to forecast events: their

accuracy could depend critically on market liquidity and trading activity. Several

researchers emphasize the potential of prediction markets to improve decisions (e.g.,

Hanson (2002), Hahn and Tetlock (2005), Sunstein (2006), and Cowgill, Wolfers, and

Zitzewitz (2007)). In principle, the range of applications is virtually limitless—from

helping businesses make better investment decisions to helping governments make better

fiscal and monetary policy decisions. For example, decision makers in the Department of

Defense, the health care industry, and multi-billion-dollar corporations, such as Eli Lilly,

General Electric, Google, France Telecom, Hewlett-Packard, IBM, Intel, Microsoft,

Siemens, and Yahoo, conduct internal prediction markets. The prices in these markets

reflect employees’ expectations about the likelihood of a homeland security threat, the

nationwide extent of a flu outbreak, the success of a new drug treatment, the sales

revenue from an existing product, the timing of a new product launch, or the quality of a

recently introduced software program.

3

Indirectly, the results shed light on the general relationship between liquidity and

absolute pricing efficiency, which could teach us something about financial markets.

Formally testing how liquidity and absolute pricing efficiency relate in conventional

financial markets would require that researchers observe securities terminal cash flows.

Even in cases where this is possible, such as in options or bond markets, other obstacles

exist. In options markets, inferences may depend critically on assumptions about the

market price of risk. In bond markets, there is often insufficient volatility in cash flows to

make the exercise interesting. By necessity, researchers in finance must rely on strong

assumptions relating absolute pricing efficiency to observable proxies for market

efficiency to estimate its relationship with liquidity. For example, many researchers argue

that liquidity increases market efficiency based on evidence from short-horizon return

predictability tests (e.g., Chordia, Roll, and Subrahmanyam (2006), and Chordia et al.

(2007)). Yet large deviations in prices from fundamentals could be associated with very

little or even no return predictability (Summers (1986)). Because nearly all efficiency

tests in equity markets do not employ measures of stocks’ fundamentals, one cannot infer

whether liquidity increases or decreases absolute pricing efficiency.

Despite these obstacles, assessing the relationship between liquidity and absolute

pricing efficiency remains important because absolute pricing efficiency—not return

predictability—determines whether capital is being efficiently allocated in financial

markets. A better understanding of the impact of liquidity on absolute pricing efficiency

could inform the decisions of firms and governments whose actions affect liquidity, and

thereby affect the efficient allocation of capital.

4

Beyond offering a particularly clean test of efficiency, there are other reasons to

expect that findings from TradeSports data are relevant for other financial markets. The

TradeSports exchange uses standard continuous double auctions, comparable to the

mechanisms used in the world’s major stock, currency, commodity and derivatives

exchanges.2 Many professional financial traders from New York, Chicago, and London

wager thousands of dollars in sports and financial markets on TradeSports.

Prices on TradeSports and conventional financial markets are likely to be

correlated. Several traders conduct automatic arbitrage transactions across conventional

exchanges and TradeSports, forcing similar pricing to prevail in these markets. Zitzewitz

(2006) reports that program trading accounts for over 95% of orders in the TradeSports

binary options securities on the daily Dow Jones index. Moreover, he finds surprising

evidence that some price discovery takes place in these daily Dow options. Specifically,

the implied volatilities from TradeSports binary options on the Dow can help forecast the

level and volatility of the Dow Jones index, even after controlling for multiple lags of

implied and historical volatilities from conventional CBOT, CBOE, and NYSE securities.

Arbitrage promotes the transmission of newly discovered price information from the

TradeSports exchange to other financial markets, and vice versa, within minutes.

There is also likely to be a common component in liquidity for similar contracts

traded on TradeSports and conventional financial exchanges because the popularity of

underlying securities indices is positively correlated across markets. For example, the

Dow securities are the most popular and actively traded on TradeSports; and the Dow

2 In both theory and practice, double auctions are particularly robust mechanisms that promote rapid

adjustment towards market equilibrium even in the presence of market frictions and trader irrationality—

e.g., Gode and Sunder (1993), Cason and Friedman (1996), Gjerstad and Dickhaut (1998), Noussair et al.

(1998), and Satterthwaite and Williams (2002).

5

stocks are also the most heavily traded stocks on the NYSE. Whatever motivates

investors to trade certain securities in one market may induce them to trade similar

securities in another market. Based on these similarities in liquidity and pricing across

markets, an understanding of the relationship between liquidity and efficiency on

TradeSports complements the indirect evidence from conventional financial markets,

where one generally cannot observe the terminal cash flows of highly volatile securities.

There are compelling theoretical reasons to think that liquidity and efficiency

could be either positive or negatively related. In many rational models of liquidity

provision, liquidity is beneficial to efficiency because it enhances the incentives for

traders to become informed and reveal their information through trading. Usually, the

indirect source of liquidity is random noise trading, which does not explicitly counteract

informed trading but does allow rational market makers to break even. An alternative

outside the scope of rational models is that some agents are naïve about the adverse

selection problem. If naïve agents submit near-market limit orders with insufficient

regard for the future release of information, they will unwittingly and systematically trade

with informed traders, effectively subsidizing liquidity provision. In such a market with

excessive liquidity provision, prices could respond more slowly to information.3

On TradeSports, I document two facts that are consistent with naïve liquidity

provision. Both facts could help to explain why forecasting accuracy is not higher in the

most liquid prediction markets, despite the strong incentives for information acquisition

and dissemination in liquid markets. First, limit orders that passively execute during

informative events have negative expected returns to expiration. This suggests that limit

3 Linnainmaa (2007) and Kaniel, Liu, Saar, and Titman (2007) report indirect evidence in financial

markets, but they cannot observe firms’ terminal cash flows. Baker and Stein (2004) and Tetlock and Hahn

(2007) present theoretical models in which liquidity subsidies lead to market underreaction.

6

orders retard the response of prices to new information and thereby inhibit forecasting

resolution. Second, limit orders traders passively buy low-priced securities—e.g., $4 and

below—and sell high-priced securities—e.g., $6 and above. Such limit orders could

sustain the overpricing of low-priced securities and the underpricing of high-priced

securities, a pattern known as the favorite-longshot bias (e.g., Thaler and Ziemba (1988)).

This second finding identifies a mechanism for how prices in liquid markets could remain

more poorly calibrated than prices in illiquid markets.

The layout of the paper is as follows. In Section II, I discuss the relationship

between this study and the prediction market and finance literatures. In Section III, I

describe the structure of the securities data from the TradeSports exchange and the

measures of liquidity used throughout the paper. In Section IV, I assess absolute pricing

efficiency in liquid and illiquid securities markets, focusing on forecasting calibration and

resolution. In Section V, I examine whether liquidity providers are naïve, documenting

the two key facts described above. In Section VI, I conclude and suggest directions for

further research on liquidity and securities market efficiency.

II. The Prediction Market Literature and Its Relationship to Finance

This study on prediction market efficiency is related to studies on the favorite-

longshot bias in wagering markets (e.g., Jullien and Selanie (2000), Wolfers and

Zitzewitz (2004), and Zitzewitz (2006)) and financial markets (e.g., Rubinstein (1985),

Brav and Heaton (1996), and Barberis and Huang (2007)). A key distinction is that these

prior studies do not link informational efficiency and market liquidity.

7

Several theoretical and empirical papers, however, do link these concepts. One

view is that illiquidity represents a transaction cost for informed arbitrageurs whose

trades make prices more efficient. For example, when liquidity increases in Kyle’s (1985)

model, informed traders bet more aggressively based on their existing information

because their trades have a smaller impact on prices. In addition, informed traders have

greater incentives to acquire more precise information in liquid markets. If informed

arbitrageurs are less active in illiquid markets where trading is expensive, securities’

prices in these markets may deviate by large amounts from their fundamental values. An

alternative view is that liquidity is a proxy for non-informational or noise trading, which

may harm informational efficiency.4 In behavioral finance models, various limits to

arbitrage prevent rational agents from making aggressive bets against noise traders—e.g.,

DeLong, Shleifer, Summers, and Waldmann (1990a) and Shleifer and Vishny (1997). If

liquid markets have more noise trading than illiquid markets and rational agents do not

fully offset noise traders’ systematic biases, then securities prices in liquid markets may

be inefficient relative to prices in illiquid markets.

Some recent papers provide indirect empirical support for the view that securities

mispricing is greater in illiquid markets—e.g., Wurgler and Zhuravskaya (2002),

Chordia, Roll, and Subrahmanyam (2006), and Chordia et al. (2007). Yet other papers

provide empirical evidence that suggests mispricing is greater in liquid markets—e.g.,

Bloomfield, O’Hara, and Saar (2007), Linnainmaa (2007), and Tetlock (2007). Of all

these papers, only Bloomfield, O’Hara, and Saar (2007) directly examines the deviation

of securities prices from fundamental values because the terminal cash flows of the

4 Variations in liquidity correspond to variations in noise trading in Kyle (1985), Glosten and Milgrom

(1985), and Baker and Stein (2004), but they may also result from variations in the search costs that buyers

and sellers incur in their efforts to transact—e.g., Duffie, Garleanu, and Pedersen (2005).

8

securities are unobservable in most real-world situations. The efficiency results from

TradeSports, where professional traders exchange large sums of money, demonstrate that

several laboratory results in Bloomfield, O’Hara, and Saar (2007) could generalize to

real-world financial markets.

III. Securities Data and Measures of Liquidity

I construct an automatic data retrieval program to collect comprehensive limit

order book and trading history statistics about each security traded on the TradeSports

exchange.5 The program runs at 30-minute intervals almost continuously from March 17,

2003 to October 23, 2006.6 All empirical tests in this paper include only data from the

single-day sports and financial securities that the program records. The vast majority of

TradeSports’ securities are based on one-day sports or financial events, such whether the

Yankees will win a particular baseball game or whether the Dow Jones Index will close

50 or more points above the previous day’s close. I focus on these securities to limit the

number of factors needed as controls in the statistical analysis that follows.7 Roughly

70% of TradeSports’ securities are based on sports events, 25% are based on financial

5 I am grateful to TradeSports Exchange Limited for granting me permission to run this program.

6 The program’s 30-minute interval is approximate because it records securities sequentially, implying that

the exact time interval depends on whether new securities have been added or subtracted and precise

download speeds. In practice, these factors rarely affect the time interval by more than two minutes. The

program stops running only for random author-specific events, such as software installations, operating

system updates, power failures, and office relocation—and technical TradeSports issues, such as daily

server maintenance and occasional changes in the web site’s HTML code. 7 For sports events, I consider only securities with an official TradeSports description that includes either

the text ―game,‖ ―bout,‖ or ―match‖; for financial events, I consider only securities based on the daily level

of stock indexes, which is the vast majority of all financial securities. Because almost all of the uncertainty

for these events is resolved during the scheduled event time, I focus on observations occurring within one

event duration of the event starting time—e.g., no more than 3 hours prior to the start of a 3-hour event.

9

events and fewer than 5% are based on events in all other categories combined—e.g.,

economic, political, entertainment, legal, weather, and miscellaneous.

The TradeSports exchange solely facilitates the trading of binary outcome

securities by its members, and does not conduct transactions for its own account.8

Securities owners receive $10 if a pre-specified, verifiable event occurs and $0

otherwise—e.g., the owner of the Dow Jones security mentioned above receives $10 if

and only if the index goes up by 50 points or more. For ease of interpretation, the

exchange divides its security prices into 100 points, worth $0.10 per point. The minimum

securities price increment, or tick size, ranges between 0.1 and one point in this sample.

TradeSports levies a commission of no more than 0.4% of the maximum

securities price ($10) on a per security basis whenever a security is bought or sold.9 At

the time of security expiration, when the payoff event is verifiable and the owner receives

payment, traders must liquidate all outstanding securities positions and incur

commissions. Note that the maximum $0.08 round-trip transaction fee is smaller than the

value of one point ($0.10) for most securities. This implies arbitrageurs have an incentive

to push prices back towards fundamental values if they stray by even one point.

Following conventions in other studies of financial markets, I eliminate

observations from TradeSports markets with poor quality price data. Specifically, I

exclude observations with a cumulative trading volume below 10 securities ($100),

market depth below 10 securities ($100), or bid-ask spreads exceeding 10% ($1.00).10

8 TradeSports limits the risk that the counterparty in a security transaction will default by imposing

symmetric margin requirements for each sale or purchase of a security by one of its members. Generally,

members must retain sufficient funds in their TradeSports account to guard against the maximum possible

loss on a transaction. TradeSports also settles and clears all transactions conducted on its exchange. 9 The exchange eliminated commissions for non-marketable limit orders on November 9, 2004.

10 The observations excluded by the combination of all three restrictions represent only 5% of volume on

the exchange. Using more stringent market activity criteria tends to strengthen the statistical results below.

10

These restrictions are designed to exclude securities without well-established market

prices for which tests of efficiency are not meaningful.

I use three measures of securities market liquidity: quoted bid-ask spreads, market

depth, and cumulative trading volume. I define the quoted spread as the difference

between the inside (lowest) ask and (highest) bid quotations. I compute market depth as

the sum of all buy and sell limit orders within the maximum 10% bid-ask spread, divided

by two. To enhance comparability across time periods and contracts, I use ad hoc cutoffs

of 1 point, 3 points, and 5 points—i.e., $0.10, $0.30, and $0.50—to partition observations

into groups sorted according to bid-ask spreads. The results are similar if I define

partitions based on the historical distribution of spreads during a rolling time window. I

follow an analogous procedure to sort securities by market depth and cumulative trading

volume, using ad hoc cutoffs of 100, 300, and 500 securities for both variables.

Table I shows that the three measures designed to capture liquidity exhibit some

similarity. The table reports the pair-wise correlations between the logarithms of quoted

spreads (LnSpread), market depth (LnDepth), and trading volume (LnVolm) for all

securities, sports securities and financial securities. All nine of the correlations in Table I

have the expected signs, and are statistically significant at the 1% level. For the group

including all securities, the volume correlations with spreads and depth are low because

the mean volume-based liquidity measure is higher in financial securities, whereas the

spread- and depth-based liquidity measures are higher in sports securities. The volume

correlations with spreads and depths are higher in the separate analyses of sports and

financial securities. The table also reports the average number of program observations

per security, which is between four and six for both sports and financial securities.

11

[Insert Table I here.]

IV. Tests of Market Efficiency

Now I analyze the absolute pricing efficiency of securities on the TradeSports

exchange. I conduct these tests separately for groups of securities sorted by each of the

three liquidity measures. I also analyze the efficiency of sports and financial markets

separately to investigate the possibility that pricing in these markets differs significantly.

Fortunately, the key results in this study apply to both sports securities and financial

securities, regardless of their exposure to market risk.11

A. Forecasting Calibration in Liquid and Illiquid Markets

Microstructure theory measures absolute pricing efficiency as the expected mean

squared error of prices minus cash flows, which can be decomposed into two components

as in Equation (1):

(1) E[(Payoff – Price)2] = E[Payoff – Price]

2 + E[(Payoff – 100 * Event Probability)

2]

First, I focus on measuring the squared bias component of absolute pricing efficiency

(i.e., the first term), as opposed to the conditional variance component (i.e., the second

term). This emphasis is standard practice in the literature on market efficiency in binary

prediction markets because expected cash flows are not directly observable for each

11

In unreported tests, I allow for the possibility that financial securities with positive exposure to market

risk have different expected returns from those with negative risk. I find a positive, but insignificant, risk

premium of less than 1% for the typical financial security with positive exposure to the market. This is not

surprising because three years of data is usually insufficient for estimating market risk premiums.

12

security. Thus, researchers cannot measure securities’ conditional variances without

making assumptions about biases, but they can estimate average biases by comparing

securities’ average cash flows to their prices. In this subsection, I estimate biases in prices

following conventions from related work—e.g., Wolfers and Zitzewitz (2004), Tetlock

(2004), and Zitzewitz (2006). In the next subsection, I make additional assumptions in an

effort to indirectly estimate the conditional variance component of mean squared error.

I employ a straightforward regression methodology to test the null hypothesis that

securities prices are unbiased predictors of securities’ cash flows. The null hypothesis is

that securities’ expected returns to expiration are zero, regardless of the current securities

price. The alternative hypothesis is that Kahneman and Tversky’s (1979) theory of

probability perception describes the pattern of expected returns across securities with

different current prices. A single observation consists of a security’s current price and its

returns until expiration. I measure current prices using the midpoints of the inside bid and

ask quotations to avoid the problem of bid-ask bounce that could affect transaction prices.

The results are robust to using the most recent transaction price instead.

I calculate a security’s percentage returns to expiration by subtracting its current

price from its payoff at expiration, which is either 0 or 100 points, then dividing by 100

points.12

This is the standard measure of returns in the prediction markets literature—e.g.,

Wolfers and Zitzewitz (2004), Tetlock (2004), and Zitzewitz (2006). Relative to

alternative measures that divide by price or the duration of the holding period, the

measure of returns to expiration described above possesses the advantages of being much

closer to homoskedastic and normally distributed, and it is symmetric for buyers and

12

I exclude the very small fraction of TradeSports contracts that do not expire at 0 or 100 points. I divide

by 100 points to represent the combined amount of capital that buyers and sellers invest in the security.

13

sellers. For the securities that I examine, the natural unit of information release is an

event, rather than a given amount of time. In addition, the opportunity cost of invested

funds is trivial over the daily time horizon of these securities.

The S-shaped form of the probability weighting function hypothesized in

Kahneman and Tversky (1979) and formalized in Prelec (1998) informs my choice of

pricing quantiles and statistical tests. The S-shape refers to a graph of subjective versus

objective probabilities, as shown first in Kahneman and Tversky (1979). Prelec (1998)

derives the S-shape in probability misperception from axiomatic foundations. His theory

predicts that agents overestimate the likelihood of events with objective probabilities less

than 1/e = 37% and underestimate the likelihood of events with objective probabilities

greater than 1/e. There is also an ample body of empirical evidence that is consistent with

a probability weighting function having a fixed point in the neighborhood of 1/e (Tversky

and Kahneman (1992), Camerer and Ho (1994), and Wu and Gonzalez (1996)).

Based on this evidence, I construct dummy variables, Price1 through Price5, for

five equally-spaced pricing intervals: (0,20), [20,40), [40,60), [60,80), and [80,100)

points. I then measure the returns until expiration for securities in each pricing quantile. I

test the null hypothesis that all returns to expiration are equal to zero against the

alternative that securities in the first two quantiles—Price1 and Price2—based on small

probability events (p < 40%), are overpriced and securities in the last three categories—

Price3, Price4, and Price5—based on large probability events (p ≥ 40%), are underpriced.

I report the results from three Wald (1943) tests based on this simple idea. The

first Wald test measures whether small probability events are overpriced on average:13

13

Despite the directional nature of over- and underpricing predicted by Kahneman and Tversky (1979) and

the favorite-longshot bias, I use two-tailed Wald tests to be conservative.

14

(2) (Price1 + Price2) / 2 = 0

The second Wald test assesses whether large probability events are underpriced:

(3) (Price3 + Price4 + Price5) / 3 = 0

The third Wald test measures whether large probability events are more underpriced than

small probability events—i.e., whether the mispricing function is S-shaped:

(4) (Price3 + Price4 + Price5) / 3 – (Price1 + Price2) / 2 = 0

Of the three, this is the most powerful test of the null hypothesis against the Kahneman

and Tversky (1979) alternative because it accounts for other factors that could influence

average returns in both small and large probability events.14

I also interpret equation (4)

as a test of the favorite-longshot bias: the expected returns on longshots, with prices less

than 40, are lower than the expected returns on favorites. In the original Ali (1977)

racetrack data, expected returns are roughly zero for horses with a 30% probability of

winning, and increase nearly monotonically with a horse’s probability of winning.

I use standard ordinary least squares to estimate the coefficients of the five pricing

categories. For all regression coefficients, I compute clustered standard errors, as in Froot

(1989), to allow for correlations in the error terms of all securities expiring on the same

calendar day, which simultaneously corrects for the repeated sampling of the same

security and the sampling of related events.15

This clustering procedure exploits the fact

that all event uncertainty is resolved on the day of expiration (see footnote 7).

To illustrate the efficiency tests and give an overview of the data, I first examine

the returns to expiration for all sports securities, all financial securities, and both groups

14

The choice of how to partition the pricing categories has little effect on the Wald tests because,

regardless of the partitioning, these tests assess whether the returns to expiration of securities priced below

40 points differ from the returns of securities priced above 40 points. 15

Using a finer clustering unit based on the expiration day and type of security does not affect the results.

15

together. Table II displays the regression coefficient estimates for Price1 through Price5

along with the three Wald tests described above. One interesting result is that neither

sports nor financial securities exhibit substantial mispricing, which is consistent with

Wolfers and Zitzewitz (2004) and Tetlock (2004).

[Insert Table II around here.]

The qualitative patterns in the pricing of both sets of securities and in their

aggregate suggest, however, that the favorite-longshot bias could play a role in any

mispricing that does exist. To aid the reader in identifying the S-shaped favorite-longshot

bias, Figure 1 provides a visual representation of mispricing in each pricing category for

sports, financial, and both types of securities.

[Insert Figure 1 around here.]

The securities based on small probability sports events in pricing quantiles 1 and

2 are slightly overpriced by 1.15 points (p-value = 0.127); and financial securities based

on large probability events in quantiles 3, 4, and 5 are underpriced by 2.21 points

(p-value = 0.030). The Wald test for the favorite-longshot bias rejects the null hypothesis

of no difference in expected returns at the 5% level for both sports and financial

securities. Interestingly, the magnitude of this bias decreases from an average of 2.13

points across the sports and financial groups to just 1.24 points in the aggregate group,

which is barely statistically significant at the 5% level. This reduction occurs because of

differences in the pricing patterns of sports and financial securities and the changing

relative composition of sports and financial securities within pricing quantiles.16

16

The disparity between the average of the individual estimates and the aggregate estimate illustrates the

importance of estimating the effects on sports and financial securities separately.

16

Having established that both sports and financial securities show a limited degree

of inefficiency on average, I now turn to the key test of whether the favorite-longshot bias

is more pronounced in illiquid or liquid securities. Panels A and B of Table III analyze

the favorite-longshot bias in sports and financial securities. The four regressions in each

panel in Table III sort securities according to their liquidity quantiles as measured by bid-

ask spreads. In both panels, the main result is that the favorite-longshot bias is no smaller

in liquid securities than the bias in illiquid securities. If anything, the bias appears larger

in liquid securities—e.g., the bias in liquidity quantiles 3 and 4 minus the bias in

quantiles 1 and 2 is positive (2.23%), but not statistically significant. Securities in the two

intermediate bid-ask spread quantiles exhibit a somewhat smaller favorite-longshot bias,

but this conclusion does not generalize for other liquidity measures. For the bid-ask

spread measure, the same patterns in the favorite-longshot bias apply to both sports and

financial securities.

[Insert Table III here.]

Based on the bid-ask spread measure, the financial securities are less liquid than

the sports securities. Panel B shows that relatively few financial securities have bid-ask

spreads less than $0.10, or 1% of the $10 maximum contract value. The financial

securities, however, are not less liquid based on the other liquidity measures, such as

limit order book depth and trading volume.

Next, I repeat the same regression analysis for sports and financial securities

sorted based on the other two liquidity measures: market depth and trading volume. For

brevity, Figure 2 summarizes only the favorite-longshot bias measures from these

17

analyses, together with the bid-ask spread results above. Figure 2 shows that the favorite-

longshot bias is virtually always positive, regardless of securities type or liquidity.

[Insert Figure 2 here.]

Overall, liquid and illiquid securities exhibit favorite-longshot biases of a similar

magnitude. In sports markets, liquid securities have slightly larger biases, but often not

significantly larger. In financial markets, the relationship between liquidity and the

favorite-longshot bias is quite weak, and depends on the liquidity measure. For example,

in financial securities with market depth in the top quantile, there is no favorite-longshot

bias; yet, in financial securities with bid-ask spreads in the bottom quantile, the favorite-

longshot bias exceeds 6%. This 6% bias is large relative to the bid-ask spreads of less

than 1% and the trading commissions of 0.8% or lower. More generally, the surprising

finding is that prices in liquid prediction markets are not better calibrated than prices in

illiquid markets.

A lack of statistical power does not seem to explain the lack of evidence for

liquidity improving efficiency. The favorite-longshot bias is consistently positive.

Moreover, the bias is actually larger in the top two liquidity quantiles than the bottom two

quantiles in five out of six cases in Figure 2. In addition, the confidence intervals are

sometimes narrow enough to reject the hypothesis that liquid securities are better

calibrated than illiquid securities at the 5% level—e.g., in the case of the trading volume

measure in sports securities. I offer a partial resolution to this puzzle in Section V.

In unreported tests, I evaluate the possibility that other security characteristics,

such as return volatility and time until expiration could explain the relationship between

mispricing and liquidity. The inclusion of the controls based on volatility and time

18

horizon does not significantly increase the explanatory power of the regressions in Table

III. Proponents of market efficiency can take comfort in the fact that few variables, other

than liquidity and price, are useful predictors of securities’ returns to expiration.

B. Forecasting Resolution in Liquid and Illiquid Markets

In this subsection, I measure how quickly securities prices converge toward event

outcomes and whether these rates depend on liquidity. In models of rational adverse

selection, periods of illiquidity tend to precede the release of information about

securities’ fundamental values and its incorporation into prices. Intuitively, traders are

reluctant to submit limit orders because they are wary that traders who submit market

orders possess information that they do not have. Thus, a lack of limit orders, or

illiquidity, could predict the release of information even if illiquidity does not cause

prices to incorporate information more rapidly.

In an effort to avoid this reverse causality problem, I estimate the impact of

liquidity on information release using instrumental variables (IV) for changes in liquidity.

Interestingly, the simple OLS estimates are qualitatively similar to the IV estimates,

suggesting that accounting for traders’ endogenous responses to time-varying adverse

selection does not affect the main findings. In Section V, I directly assess how limit order

traders respond to time-varying information release.

I use two instruments for market design that could have a significant impact on

prediction market liquidity, but do not have a direct impact on the release of event

information in sports and financial markets. On September 1, 2004, the TradeSports

19

exchange began a series of three changes in its trading fee structure. First, the exchange

reduced the trading fees on securities priced above $9.50 or below $0.50 by half. Within

two weeks, the exchange reduced the minimum tick size on its securities from $0.10 to

$0.01. Finally, on November 9, 2004, the exchange eliminated all trading fees on limit

orders that did not immediately execute. I construct two dummy variables to instrument

for changes in liquidity that occurred during the transition phase, September 1, 2004 to

November 9, 2004, and for changes occurring after all new rules were implemented. I use

observations on securities from March 1, 2004 through February 9, 2005 to evaluate the

impact of these changes.17

I measure the extent of information release during an event as the convergence of

prices toward securities’ terminal payoffs at expiration—i.e., the reduction in the squared

difference between prices and terminal payoffs. To analyze the change in this squared

difference, I use the identity in Equation (1) that decomposes mean squared error into

squared bias (calibration) and conditional variance (resolution) components.

The measurement of information release as the reduction in mean squared pricing

error (MSPE) requires an important assumption: reductions in MSPE occur only from

reduction in the conditional variance component—i.e., the squared bias component does

not change. This may be a reasonable approximation for short time horizons, but the

previous results suggest this assumption could fail for long time horizons because

squared bias approaches zero as an event ends. Specifically, if liquid markets exhibit a

greater favorite-longshot bias that is corrected over time, periods of liquidity will appear

17

Because an idiosyncratic author-specific event limits the number of observations in the pre-event period,

I use a six-month pre-event window to obtain a similar number of observations before and after the two

rule changes. The key regression coefficients are quantitatively sensitive to the specific event window

chosen, but the qualitative conclusions are robust.

20

to precede greater information release even if there is no causal relationship between the

two. This reasoning suggests my assumption biases the results toward finding that

liquidity causes prices to incorporate information more rapidly—but the bias is small

because there is not a large difference in mispricing between liquid and illiquid markets.

I use a two-stage least squares approach to examine how liquidity and the rate of

price convergence change as TradeSports changes its market design. I control for several

factors other than liquidity that influence the release of event information. For each sports

and financial security, I create a continuous scaled measure of the event time: event time

= current time – event start time / (event duration). I then create a series of dummy

variables to indicate the discrete event time position of a security in 20% increments,

where EvTime_X corresponds to an event time interval of ((X-1)*0.2, X*0.2] and X = 0, 1,

…, 6. Although some sports events last longer than expected, financial events almost

never do because they are based on index levels at pre-specified times. I also control for

the logarithm of the event time, in case the dummies fail to capture within-event trends in

liquidity or information release. In addition, I control for the logarithm of the date on

which the event is scheduled to expire to ensure that the excluded market design

instruments do not capture long-term trends in liquidity and information release.

Finally, I include a control for expected information release (ExpInfo) based on

the current securities price level. ExpInfo is defined as (100 – Price) * Price, which is the

expected value of squared pricing error under the assumption of market efficiency. To see

this, note that market efficiency implies prices equal true event probabilities, so that

Equation (5) holds:

21

(5) E[(Payoff – Price)2] = E[(Payoff – 100 * Event Probability)

2]

= (100 – Event Probability) * Event Probability = (100 – Price) * Price

In robustness checks, I find that the liquidity coefficient estimates are not particularly

sensitive to the use of alternative sets of control variables.

Table IV reports the results from six IV regressions each of which measures the

causal effect of liquidity on the reduction in MSPE over the next data recording period

(roughly 30 minutes). The six (2 x 3) IV regressions correspond to the results for sports

and financial securities for each of the three measures of liquidity: the logarithms of bid-

ask spreads (LnSpread), market depth (LnDepth), and trading volume (LnVolm). All

standard errors in Table IV are robust to heteroskedasticity and arbitrary intra-group

correlation within securities that expire on the same day (Froot (1989)).

[Insert Table IV here.]

Table IV consistently shows that an increase in liquidity slows the rate at which

prices incorporate event information. In four out of six IV regressions, I reject the null

hypothesis of no effect with a 1% Type I error; and, in the other two regressions, I reject

the null at the 10% level. The coefficient estimates are reasonably similar across the six

specifications. As bid-ask spreads decline, as market depth goes up, and as trading

volume increases, MSPE decreases more slowly. In all six specifications, the magnitude

of the effect is between 200 and 600 squared percentage points of MSPE per one standard

deviation increase in liquidity. To think about this magnitude, consider a security priced

at 55 that will eventually expire at 100, implying that the initial MSPE is 2025 points. A

drop in bid-ask spreads from 4 points to 2 points is roughly one standard deviation. On

average, this decrease in the spread would prevent the security priced at 55 from

22

converging to a price of 60—a new MSPE of 1600 points, which is 425 points lower—in

the next 30 minutes. In other words, the decrease in information release can be larger

than the increase in spreads.

Regression misspecification does not seem to explain this puzzling finding. Table

IV shows that I cannot reject any of the six overidentifying restrictions for the excluded

instrument at even the 10% level—see the Hansen (1982) J-statistics, which have a chi

squared distribution with one degree of freedom. In addition, the regression equations are

not underidentified: the Andersen (1984) likelihood-ratio statistic strongly rejects

underidentification in all six cases. Finally, a comparison of the Cragg-Donaldson

F-statistic to either the Cragg-Donaldson (1993) or the Stock and Yogo (2005) critical

values shows that the two instruments are not weak.

The intuition for the IV estimates is that the change in TradeSports’ market design

causes opposing changes in the speed of price responses and market liquidity. These

opposing changes occur in both sports markets and financial markets. Interestingly,

although TradeSports’ new rules increase all three measures of liquidity in financial

markets, they actually decrease all three measures of liquidity in sports markets (after

controlling for other factors). One possible explanation is that the optimal tick size differs

in sports and financial securities (e.g., Harris (1991) and Angel (1997)). As liquidity

increases in financial markets, prices respond more slowly to information; and, as

liquidity decreases in sports markets, prices respond more quickly to information.

23

V. Exploring the Liquidity Provision Mechanism

The evidence in Section IV suggests that forecasting calibration is not better in

liquid prediction markets, and that resolution is actually worse. This is surprising because

liquid markets generally provide greater incentives for traders to acquire and act on

information, whereas illiquid markets inhibit informed trading. In an effort to understand

the two main findings in Section IV, I study the mechanism whereby prices incorporate

information in prediction markets. I gather comprehensive trade-by-trade data from the

TradeSports Exchange Limited archive to monitor how prices respond to information.

This individual trade data indicates whether the buyer or seller initiated the trade.

Because the TradeSports exchange operates as a pure limit order book, I deduce that the

party initiating the trade submitted a market order (or a marketable limit order), and the

counterparty initially submitted a (non-marketable) limit order.

Two key properties of the limit orders that execute shed light on the liquidity

provision mechanism. First, during periods of frequent trading activity, limit orders that

execute have negative expected returns. This suggests that market orders during these

time periods convey valuable information that prices do not fully incorporate, perhaps

because limit orders naively stand in the way of price discovery. Second, limit order

traders passively buy low-priced securities and sell high-priced securities. This suggests

that traders submitting market orders exploit and counteract the favorite-longshot bias,

but that standing limit orders delay the correction in prices.

24

A. Limit and Market Order Behavior during Informative Events

First, I analyze the performance of active (market order) and passive (limit order)

trades when traders act on event-relevant information. Although I do not directly observe

event-relevant information, I develop a simple empirical proxy based on the clustering of

trades during time periods when the event is scheduled to be in-progress. The

TradeSports exchange supplies the official starting and ending event times—e.g., a

typical baseball game lasts 3 hours; and a typical financial index event lasts from 9:30am

Eastern time to 4:00pm Eastern time.

Table V summarizes the daily performance of market orders that trigger trades on

the TradeSports exchange. I define a time period to be informative if the preceding three

trades occurred within 60 seconds of each other and the event is currently in-progress. I

define a time period to be uninformative if the preceding three trades did not occur within

10 minutes of each other and the event is not yet in-progress. On each day, I aggregate

the properties of the trades in both groups from the perspective of the market order trader.

The value-weighted statistics weight trades by the number of securities traded, whereas

equal-weighted statistics weight trades equally. Table V reports the daily averages of

several trading statistics for the trades during informative periods, uninformative periods,

and all periods. I form these three groups separately within sports and financial securities.

The goal of this analysis is to assess whether traders submitting market orders or limit

orders receive and act on superior information during periods of high adverse selection.

[Insert Table V here.]

25

The main finding in Table V is that the trader submitting the market order

consistently outperforms the limit order trader following trade clusters during the event.

The magnitude of the market order trader’s value-weighted daily return is greater than

1% and highly statistically significant for both sports and financial securities. These

returns to expiration narrowly exceed the maximum round-trip commission costs of 0.8%

for market orders.

Interestingly, when the prior three trades are not clustered within a 10-minute

period and the event is not taking place, limit order traders perform significantly better

than market order traders. In these situations, the returns to expiration for limit order

traders are 0.77% and 1.12% for sports and financial securities, and are statistically

significant at the 5% level. In addition, limit order traders incur commissions of no more

than 0.4% upon expiration, and incur no commission on the initial trade after November

9, 2004. Thus, their returns to expiration are positive even after including fees.

The main result in Table V is robust to several alternative methodological

approaches. The second row of Table V shows that using equal-weighted returns, rather

than weighting each trade by the quantity traded, generates qualitatively similar results.

The third row (EW Return w/ Lag) shows that a market order trader can use public

information about past trades to exploit the market friction during informative time

periods. This row computes the hypothetical equal-weighted return for a trader taking the

same position in the current trade as the previous market order trader—e.g., taking the

buy-side of the current trade if the previous trade was buyer-initiated. The strongly

positive and significant return for this strategy shows that lags in price discovery prevent

complete adjustment to the direction of trade initiation. In unreported tests, I find that

26

prices only partially adjust to the initiation direction of the previous five trades. In

addition, sorting trades according to alternative proxies for information—e.g., using

recent price volatility instead of recent trading clustering—produces results qualitatively

similar to those in Table V.18

An implication of Table V is that limit order traders are systematically losing

money in time periods when prices are incorporating new information. It is as though

these traders pay insufficient attention to time-varying adverse selection. During

informative periods, limit order traders provide liquidity in excessive amounts relative to

a competitive market maker who tries to break even on each transaction. This naïve

liquidity provision, or failure to withdraw liquidity, delays the response of prices to

informative market order flows during the event. Still, during uninformative pre-event

periods, liquidity can be beneficial for market efficiency, as shown in columns Two and

Five in Table V: limit order traders prevent the overreaction of prices to uninformative

market orders during these periods. Figure 3 visually depicts these patterns in returns to

expiration around informative and uninformative events. The key point is that limit order

trades are associated with less efficient pricing during informative event periods, but

more efficient pricing during quiescent pre-event periods.

[Insert Figure 3 here.]

As an aside, the buy-sell imbalance row in Table V shows that there are more

buyer-initiated trades in both sports and financial securities, mainly during the pre-event

periods without trading clusters. I define buy-sell imbalance as the difference in the

quantities of buyer- and seller-initiated trades divided by the total quantity of trades.

18

Row four in Table V reveals that are far more market buy orders than market sell orders in pre-event

periods without clustered trades. This imbalance could indicate that aggressive pre-event traders suffer

from a framing bias, but I have no additional evidence to support this theory.

27

Because margin requirements and limits on trading are symmetric on the exchange, they

cannot explain the asymmetry between buyers’ and sellers’ aggressive market orders.

Thus, the positive buy-sell imbalance suggests that the preferences or prior beliefs of

aggressive pre-event traders are aligned with the way the TradeSports exchange frames

the events underlying securities—e.g., pre-event traders prefer to buy or speculatively

buy the security based on the Dow going up when the underlying event is framed as the

Dow going up, rather than down. However, the framing effect is much larger for

securities with negative risk exposure, suggesting that pre-event hedging explains much

of the effect in financial securities. Because TradeSports’ choices of event frames are not

random, it is unclear whether this framing effect is causal—but other researchers have

found a causal framing effect in similar contexts (Fox, Rogers, and Tversky (1996)).

B. Limit and Market Order Behavior across Pricing Quantiles

Next, I investigate whether limit orders could impede the response of prices to

aggressive market order traders who exploit market inefficiencies, such as the favorite-

longshot bias. The purpose of these tests is to reconcile the lack of evidence for better

forecasting calibration in liquid prediction markets in Section IV with the strong

incentives for informed trading that liquidity provides. Specifically, I explore the

possibility that limit order traders exhibit a systematic behavioral tendency that could

offset the beneficial impact of improvements in liquidity.

28

To test this hypothesis, I examine how the quantities of limit buy and sell orders

vary according to the prices of these binary-outcome (0 or 100 points) securities. I sort

both sports and financial securities into the five 20-point pricing quantiles described

earlier. For each of these ten (2x5) groups of securities, I aggregate the buy-sell

imbalance and returns over all trades taking place during scheduled event times. Again, I

aggregate trades on a daily basis from the perspective of the trader submitting the market

order. Panels A and B in Table VI report the value-weighted buy-sell imbalance and

returns for each of the pricing quantiles. I use the securities price from the previous

transaction as the basis for these sorts to avoid any mechanical correlation induced by

price pressure or bid-ask bounce. The results are slightly stronger if I use the

contemporaneous transaction price instead.

Table VI reveals that the patterns in the buy-sell imbalances of market orders are

similar to the favorite-longshot patterns in expected returns across pricing quantiles.

Market order traders in both sports and financial securities are more likely to sell

(longshot) securities with prices below 40 points, which have lower expected returns than

other securities. Market order traders tend to buy (favorite) securities priced above 60

points (or above 40 points in sports securities), which have higher expected returns than

other securities. The buy-sell imbalance results in Table VI demonstrate that limit order

traders may systematically, albeit passively, exacerbate the favorite-longshot bias in

prices. Executed limit orders tend to buy overpriced longshots and sell underpriced

favorites in both sports and financial securities. This tendency is strong in economic

terms: in sports securities purchases account for 55.6% and 43.7% of trades in pricing

29

quantiles 2 and 4, respectively; in financial securities, purchases account for 54.1% and

46.3% of trades in pricing quantiles 2 and 4, respectively.

Table VI also shows that market orders have significantly positive expected

returns in most pricing quantiles, suggesting market orders are based on superior

information. Expected returns in the middle pricing quantiles generally exceed expected

returns in the extreme quantiles. One interpretation is that the securities in the middle

quantiles have higher conditional variances—e.g., in an efficient market, conditional

variance is Price*(100 – Price), which is maximized at Price = 50 points—and limit

order traders do not set appropriately wide bid-ask spreads to account for this fact.

Lastly, I try to determine whether the favorite-longshot pattern in limit order

execution is active or passive by looking at order imbalances in the limit order book. Two

facts could explain the relatively large quantities of executed limit buy orders for

longshots: either limit traders submit more buy orders for longshots than for favorites, or

market order traders selectively sell to the limit order traders who submit buy orders for

longshots. In the first explanation, the buy-sell imbalance of unexecuted limit orders

should be higher for longshots than for favorites, whereas the second explanation predicts

a lower buy-sell imbalance for longshots. To test these explanations, on each day, I

compute the limit order book statistics using the same procedure described earlier for

trades. The only difference is that I use market depth rather than trading quantities to

generate value-weighted statistics.

[Insert Table VII here.]

Most of the evidence in Table VII supports the passive explanation of limit order

traders’ buy-sell imbalances, particularly in the financial securities shown in Panel B.

30

Sell-side limit orders are conspicuously missing in increasing amounts at higher pricing

quantiles, mimicking the patterns of buyer-initiated market order trades in Table VI. In

financial securities in Panel B of Table VII, the difference in buy-sell imbalances across

the pricing quantiles is highly statistically and economically significant—e.g., the

percentage of unexecuted limit sell orders is 12.4% lower in pricing quantile 1 than in

pricing quantile 5. The decreases in depth and increases in volume at higher pricing

quantiles reinforce the interpretation that buyer-initiated market orders actively take sell-

side liquidity away from high-priced securities. These trading patterns are less obvious in

the sports securities in Panel A of Table VII, though they appear within the top three

pricing quantiles. In the bottom two pricing quantiles, there is some evidence to suggest

that sports traders actively submit limit orders to purchase longshots.

[Insert Figure 4 here.]

Figure 4 summarizes the results on market and limit order buy-sell imbalances in

Table VI and Table VII. The solid and dashed black lines, describing financial market

order and limit order imbalances across the five pricing quantiles, correlate strongly with

each other (0.56). By contrast, the solid and dashed gray lines, describing sports market

order and limit order imbalances, are weakly positively correlated (0.13). In both cases,

the evidence is broadly consistent with the naïve and passive explanation of limit order

trader behavior.19

19

In unreported tests, I show that buy-sell imbalances in unexecuted limit orders do not predict event

outcomes, providing further confirmation that unexecuted limit orders are not informed.

31

VI. Concluding Discussion

This study’s main contribution is to illustrate the complex efficiency

consequences of liquidity provision, exploiting the simple structure of securities in

prediction markets with observable terminal cash flows and limited exposure to

systematic risks. In both sports and financial prediction markets, the calibration of prices

to event probabilities does not improve with increases in liquidity; and the forecasting

resolution of market prices actually decreases with increases in liquidity.

A careful examination of the behavior of limit order traders, who provide

liquidity, shows that these agents do not conform to the assumptions in standard rational

models. In times when market order flow is informative, limit order traders supply

liquidity in excessive amounts, systematically losing money to market order traders. This

finding could help to explain why prices in liquid markets are slow to incorporate event

information. Furthermore, limit order traders passively trade against the favorite-longshot

bias, possibly explaining why prices in liquid prediction markets are not better calibrated

than prices in illiquid markets.

More broadly, these results show that liquidity providers are not always rational,

and do not always attain zero profits. The findings also suggest that traders’ passivity and

naïveté partially explain underreaction to information in prediction markets. Given that

Linnainmaa (2007) observes similar behavioral and pricing phenomena in financial

markets, the same limit order mechanism could hinder efficiency in financial markets

with unusually high depth.

32

Anecdotally, cases such as technology stocks during the Internet boom raise

doubts about whether pricing in liquid markets is always more efficient than pricing in

illiquid markets. Further exploration of the limit order mechanism identified here and in

Linnainmaa (2007) could yield insights into these puzzling cases. The effect of excessive

liquidity provision on equilibrium prices depends critically on how arbitrageurs respond

to liquidity. Because liquidity gives arbitrageurs the option to enter and exit their trading

positions easily, it could induce them to take short-run outlooks and conduct trades that

actually exacerbate mispricing (e.g., DeLong et al. (1990b) and Brunnermeier and Nagel

(2004)). In other cases in which arbitrageurs have incentives to correct mispricing, they

may be unable to do so because they have less capital than naïve liquidity providers.

Theoretical models of the limit order mechanism could make new predictions about the

situations in which liquid markets are more or less efficient than illiquid markets.

33

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37

Table I: Summary of Liquidity Statistics for Prediction Market Securities

All securities are based on one-day binary outcome events: either sports games or levels

of financial indexes. At 30-minute intervals, a web crawler records statistics for all

securities in which active trading occurs from March 17, 2003 to October 23, 2006. Table

I summarizes three measures of securities market liquidity: quoted bid-ask spreads,

market depth, and cumulative trading volume—see text for definitions. The table reports

the pair-wise correlations between the logarithms of quoted spreads (LnSpread), market

depth (LnDepth), and trading volume (LnVolm) for all securities, sports securities and

financial securities. The means for each liquidity measure are equal-weighted (EW)

across all order book observations.

Securities Included All Sports Financial

Correlations LnSpread-LnDepth -0.434 -0.334 -0.208

LnSpread-LnVolm -0.012 -0.101 -0.205

LnDepth-LnVolm 0.124 0.177 0.414

Means EW Spread 2.51 2.08 4.37

EW Depth 537 605 238

EW Volume 455 405 674

# of Observations 247613 201492 46121

# of Securities 46670 35089 11581

38

Table II: Returns to Expiration for Sports and Financial Securities

This table reports the results from three ordinary least squares (OLS) regressions of

securities’ returns to expiration on five dummy variables, representing five equally-

spaced pricing intervals: (0,20), [20,40), [40,60), [60,80), and [80,100) points.. The three

regressions include observations of the returns and prices of securities based on one-day

sports, financial, and all events recorded at 30-minute intervals in which there is active

trading. I compute returns to expiration as the payoff at expiration, 0 or 100 points, minus

the bid-ask midpoint divided by 100 points. The small probabilities row displays the

magnitude and significance of the average coefficient on Price1 and Price2. The large

probabilities row displays the magnitude and significance of the average coefficient on

Price3, Price4, and Price5. The large minus small row reports the magnitude and

significance of the difference in these two averages. Standard errors clustered for

securities that expire on the same calendar day appear in parentheses (Froot (1989)). The

symbols *, **, and *** denote significance at the 10%, 5%, and 1%, levels, respectively.

Sports Financial All

0 < Price < 20 -1.65** -0.30 -0.55

(0.67) (0.63) (0.53)

20 ≤ Price < 40 -0.64 -0.23 -0.46

(1.25) (1.12) (0.87)

40 ≤ Price < 60 -0.65 2.47* -0.48

(0.53) (1.41) (0.50)

60 ≤ Price < 80 0.82 2.81** 1.09

(0.88) (1.42) (0.78)

80 ≤ Price < 100 1.73** 1.34 1.60***

(0.81) (0.82) (0.59)

Small Probabilities -1.15* -0.27 -0.50

(0.75) (0.79) (0.59)

Large Probabilities 0.63 2.21** 0.74*

(0.52) (1.02) (0.44)

Large – Small 1.78** 2.47** 1.24*

(0.83) (1.03) (0.68)

R2 0.0003 0.0016 0.0003

Expiration Days 1110 707 1122

Observations 201492 46121 247613

39

Table III: Returns to Expiration for Sports and Financial Securities Sorted by Bid-Ask Spread

This table reports the results from eight (2x4) ordinary least squares (OLS) regressions of securities’ returns to expiration on five

dummy variables (Price1 to Price5), representing five equally-spaced pricing intervals: (0,20), [20,40), [40,60), [60,80), and [80,100).

The eight regressions include two sets of regressions for securities based on one-day binary outcome sports and financial events. Each

set includes regressions for groups of securities sorted into four quantiles by their bid-ask spreads (S). The small, large, and small

minus large probabilities rows display the magnitude and significance of the average coefficients on Price1 and Price2, Price3, Price4,

and Price5, and their difference, respectively. Standard errors clustered for securities that expire on the same calendar day appear in

parentheses (Froot (1989)). The symbols *, **, and *** denote significance at the 10%, 5%, and 1%, levels, respectively.

Sports Securities Financial Securities

Bid-Ask Spread (S) S ≤ 1 1 < S ≤ 3 3 < S ≤ 5 S > 5 S ≤ 1 1 < S ≤ 3 3 < S ≤ 5 S > 5

0 < Price < 20 -3.42*** -1.15 -1.35 -0.91 -0.09 -0.61 -0.19 -0.31

(1.26) (1.00) (1.01) (1.40) (1.34) (0.76) (0.73) (0.77)

20 ≤ Price < 40 -2.22 -0.58 1.06 -2.64 -5.05 2.05 0.71 -1.15

(3.67) (1.42) (1.52) (1.62) (4.64) (1.92) (1.50) (1.14)

40 ≤ Price < 60 -1.06 -0.45 -0.84 -0.89 5.87 2.26 -0.47 3.98***

(1.16) (0.58) (0.55) (0.88) (5.43) (2.35) (1.81) (1.50)

60 ≤ Price < 80 0.92 0.88 0.19 1.94 2.41 5.15** 0.97 3.33**

(1.77) (0.95) (1.05) (1.38) (4.93) (2.17) (1.87) (1.53)

80 ≤ Price < 100 2.79 1.39 1.45 2.28** 2.33** 1.23 1.41 1.24

(1.87) (1.07) (0.96) (0.98) (0.92) (1.21) (0.88) (1.05)

Small Probabilities -2.82 -0.87 -0.15 -1.77 -2.57 0.72 0.26 -0.73

(1.92) (0.93) (0.96) (1.12) 2.47 (1.16) (1.00) (0.83)

Large Probabilities 0.88 0.61 0.27 1.11 3.54 2.88** 0.64 2.85***

(1.06) (0.59) (0.57) (0.68) (2.42) (1.41) (1.23) (1.10)

Large – Small 3.70* 1.47 0.41 2.89** 6.11* 2.16 0.37 3.58***

(2.20) (1.03) (1.03) (1.24) (3.45) (1.51) (1.22) (1.18)

R2 0.0008 0.0002 0.0003 0.0011 0.0096 0.0038 0.0004 0.0033

Expiration Days 634 1099 1100 998 351 616 669 696

Observations 30818 112839 43380 14455 839 6218 15811 23253

40

Table IV: The Effect of Liquidity on the Convergence of Prices to Outcomes

This table reports the results from six two-stage least squares regressions of the reduction in squared percentage returns to expiration

on liquidity and several control variables. I compute the reduction in squared returns over the 30-minute period following liquidity and

control variable measurement. The key independent variables are the logarithms of bid-ask spreads (LnSpread), market depth

(LnDepth), and trading volume (LnVolm). I use two dummy variables to instrument for changes in liquidity using TradeSports market

design changes on September 1, 2004 and November 9, 2004. Each regression uses observations from March 1, 2004 to February 9,

2004. I include a control variable for an event’s expected information release through expiration, ExpInfo, which is (100 – Price) *

Price. All regressions also include controls for six event time dummies, an event time trend, and a date trend. The Anderson, Cragg-

Donaldson, and Hansen test statistics for underidentification, weak identification, and overidentification appear below, along with

appropriate p-values and critical values. Standard errors clustered for securities that expire on the same calendar day appear in

parentheses (Froot (1989)). The symbols *, **, and *** denote significance at the 10%, 5%, and 1%, levels, respectively.

MSPE Reduction in Sports MSPE Reduction in Financial

LnSpread 310*** 978**

(90) (445)

LnDepth -284*** -465*

(85) (242)

LnVolm -189*** -188*

(47) (108)

ExpInfo 0.23*** 0.25*** 0.13*** 0.13* 0.23*** 0.24***

(0.04) (0.04) (0.04) (0.07) (0.04) (0.04)

Anderson LR 711.8*** 541.3*** 405.4*** 42.8*** 125.5*** 151.3***

Anderson p-value 0.000 0.000 0.000 0.000 0.000 0.000

Cragg-Donaldson F 364.4*** 275.5*** 205.3*** 21.5*** 63.7*** 77.1***

F for 10% IV Size 19.9 19.9 19.9 19.9 19.9 19.9

Hansen J 0.15 3.07* 0.02 0.65 1.16 2.52

Hanson p-value 0.694 0.080 0.884 0.420 0.282 0.112

R2 0.231 0.226 0.225 0.010 0.075 0.090

Expiration Days 232 232 232 163 163 163

Observations 14644 14644 14644 3294 3294 3294

41

Table V: Market Order Performance after Informative and Uninformative Periods

Table V summarizes the average daily returns to expiration of market orders that trigger

trades on the TradeSports exchange. The columns report these statistics for the trades

during ―Info‖ periods, during ―No Info‖ periods, and all trades. I form these three groups

separately within sports and financial securities. The ―Info‖ trades are those occurring

during the event and after three trades occurring within 60 seconds of each other. The

―No Info‖ trades are those occurring before the event and after three trades that did not

occur within 10 minutes of each other. On each day, I aggregate the properties of the

trades in all groups from the perspective of the market order trader. The value-weighted

(VW) statistics weight trades by the number of securities traded, whereas equal-weighted

(EW) statistics weight trades equally. The ―EW Return w/ Lag‖ row computes the

hypothetical equal-weighted return to expiration for a trader taking the same position in

the current trade as the previous market order trader. I define the VW buy-sell imbalance

as the quantity of buyer-initiated trades minus the quantity of seller-initiated trades

divided by the total quantity of trades. Standard errors in parentheses are robust to

heteroskedasticity and autocorrelation up to five lags (Newey and West (1987)).

Sports Financial

Info No Info All Info No Info All

VW Return 1.20*** -0.77** 0.38*** 1.41*** -1.12** 0.35***

(0.28) (0.34) (0.12) (0.30) (0.56) (0.10)

EW Return 0.48** -0.54*** 0.07 0.94*** -0.98*** 0.29***

(0.22) (0.18) (0.08) (0.17) (0.34) (0.06)

EW Return w/ Lag 0.91*** -0.16 0.26*** 0.53*** -0.12 0.34***

(0.21) (0.18) (0.09) (0.18) (0.35) (0.06)

VW Buy-Sell Imbal 0.005 0.217*** 0.067*** 0.013 0.062*** -0.001

(0.008) (0.008) (0.004) (0.009) (0.015) (0.003)

# Trades 308 208 1485 303 48 1429

Days 1518 1540 1546 1080 1051 1089

42

Table VI: Market Order Imbalances and Returns Sorted by Pricing Quantile

Table VI summarizes the average daily returns to expiration and buy-sell imbalances of

market orders that trigger trades on the TradeSports exchange. I sort both sports (Panel

A) and financial (Panel B) securities into five equally-spaced pricing quantiles—(0,20),

[20,40), [40,60), [60,80), and [80,100)—using the securities price from the previous

transaction. For each of these ten (2x5) groups of securities, I aggregate each day’s buy-

sell imbalance and returns for all trades taking place during the scheduled event time. I

compute the properties of the trades in the ten groups from the perspective of the market

order trader. The value-weighted (VW) statistics weight trades by the number of

securities traded. Table VI reports these daily averages of trading statistics for the ten

groups of securities. I define the VW buy-sell imbalance as the quantity of buyer-initiated

trades minus the quantity of seller-initiated trades divided by the total quantity of trades.

Standard errors in parentheses are robust to heteroskedasticity (White (1980)).

Panel A: Sports Securities

0 < P < 20 20 ≤ P < 40 40 ≤ P < 60 60 ≤ P < 80 80 ≤ P < 100

VW Buy-Sell Imbal -0.167*** -0.112*** 0.059*** 0.127*** 0.166***

(0.009) (0.008) (0.005) (0.007) (0.008)

VW Return -0.04 1.44*** 0.64*** 0.89*** 0.48*

(0.31) (0.35) (0.23) (0.29) (0.26)

# Trades 153 178 412 242 160

# Days 1511 1531 1543 1539 1515

Panel B: Financial Securities

0 < P < 20 20 ≤ P < 40 40 ≤ P < 60 60 ≤ P < 80 80 ≤ P < 100

VW Buy-Sell Imbal -0.016* -0.081*** 0.000 0.074*** 0.054***

(0.009) (0.006) (0.006) (0.008) (0.009)

VW Return 0.03 0.21 0.74*** 0.76*** 0.40

(0.25) (0.28) (0.25) (0.27) (0.31)

# of Trades 298 302 298 228 198

# of Days 1082 1081 1080 1075 1059

43

Table VII: Unexecuted Limit Orders Sorted by Pricing Quantile

Table VII reports average daily statistics from the TradeSports order book recorded at 30-

minute intervals. I sort both sports (Panel A) and financial (Panel B) securities into five

equally-spaced pricing quantiles—(0,20), [20,40), [40,60), [60,80), and [80,100)—using

the securities price from the previous transaction. For each of these ten (2x5) groups of

securities, I aggregate each day’s buy-sell imbalance and order book liquidity across all

data recording periods. The value-weighted (VW) statistics weight observations by order

book depth, whereas the equal-weighted (EW) statistics weight observations equally. See

text for details on buy-sell imbalance, depth, volume, and spread definitions. Standard

errors in parentheses are robust to heteroskedasticity (White (1980)).

Panel A: Sports Securities

0 < P < 20 20 ≤ P < 40 40 ≤ P < 60 60 ≤ P < 80 80 ≤ P < 100

VW Buy-Sell Imbal 0.045* 0.085*** 0.012*** 0.034*** 0.117***

(0.026) (0.012) (0.004) (0.007) (0.014)

EW Buy-Sell Imbal 0.051** 0.087*** 0.019*** 0.047*** 0.138***

(0.026) (0.011) (0.004) (0.006) (0.014)

EW Depth 394*** 476*** 641*** 616*** 475***

(13) (16) (9) (10) (10)

EW Volume 3393*** 1683*** 422*** 640*** 1629***

(168) (95) (17) (36) (82)

VW Bid-Ask Spreads 2.67*** 2.56*** 1.93*** 2.00*** 2.48***

(0.07) (0.05) (0.02) (0.03) (0.04)

EW Bid-Ask Spreads 2.75*** 2.74*** 2.13*** 2.20*** 2.62***

(0.07) (0.05) (0.02) (0.03) (0.04)

# of Days 490 784 1089 1001 745

Panel B: Financial Securities

0 < P < 20 20 ≤ P < 40 40 ≤ P < 60 60 ≤ P < 80 80 ≤ P < 100

VW Buy-Sell Imbal 0.030** 0.117*** 0.134*** 0.158*** 0.278***

(0.016) (0.010) (0.008) (0.011) (0.018)

EW Buy-Sell Imbal 0.000 0.130*** 0.161*** 0.185*** 0.303***

(0.017) (0.010) (0.009) (0.011) (0.017)

EW Past Depth 279*** 278*** 263*** 250*** 238***

(7) (7) (6) (6) (6)

EW Past Volume 1009*** 990*** 1103*** 1106*** 1335***

(55) (37) (50) (48) (65)

VW Bid-Ask Spreads 3.95*** 4.32*** 4.29*** 4.29*** 3.99***

(0.05) (0.05) (0.05) (0.06) (0.06)

EW Bid-Ask Spreads 4.08*** 4.49*** 4.53*** 4.51*** 4.11***

(0.05) (0.05) (0.05) (0.05) (0.06)

# of Days 516 535 581 585 522

44

Figure 1: The Favorite-Longshot Bias in Sports and Financial Securities

This figure depicts the estimated returns to expiration of securities based on one-day

events for five equally-spaced pricing quantiles: (0,20), [20,40), [40,60), [60,80), and

[80,100). The three series in the figure depict the returns of securities based on sports

events, financial events, and all events combined. Thus, the figure plots the three sets of

coefficient estimates on the five pricing category coefficients shown in the three columns

in Table II (see table for construction).

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

1 2 3 4 5

Ret

urn

s to

Ex

pir

atio

n

Pricing Quantile

Sports

Financial

All

45

Figure 2: The Effect of Liquidity on Returns to Expiration

This figure depicts the estimated favorite-longshot biases in returns to expiration of sports

and financial securities with differing degrees of liquidity as measured by three proxies—

bid-ask spreads, market depth, and trading volume. I measure favorite-longshot biases for

securities in each of the four bid-ask spread quantiles, where the bias is the expected

returns on favorites minus the expected returns on longshots—see Table III and the text

for details. I perform analogous tests for securities within each market depth and trading

volume quantile.

-1.00

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

1 2 3 4

Fav

ori

te-L

ongsh

ot

Bia

s in

Ret

urn

s to

Ex

pir

atio

n

Liquidity Quantile

Sports Spreads

Financial Spreads

Sports Depth

Financial Depth

Sports Volume

Financial Volume

46

Figure 3: Market Order Performance after Informative and Uninformative Periods

This figure summarizes the average daily returns to expiration for market orders that

trigger trades on the TradeSports exchange. Figure 3 reports these statistics for the trades

during ―Info‖ periods, during ―No Info‖ periods, and all trades. I form these three groups

separately within sports and financial securities. The ―Info‖ trades are those occurring

during the event and after three trades occurring within 60 seconds of each other. The

―No Info‖ trades are those occurring before the event and after three trades that did not

occur within 10 minutes of each other. On each day, I aggregate the properties of the

trades in all groups from the perspective of the market order trader. The value-weighted

(VW) return series weights trades by the number of securities traded, whereas equal-

weighted (EW) return series weights trades equally. The ―EW Return w/ Lag‖ data series

computes the hypothetical equal-weighted return to expiration for a trader taking the

same position in the current trade as the previous market order trader.

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

Sports

Info

Sports

No Info

Sports

All

Financial

Info

Financial

No Info

Financial

All

Ret

urn

s to

Ex

pir

atio

n i

n P

erce

nt

Group of Securities

VW Return

EW Return

EW Return w/ Lag

47

Figure 4: Buy-Sell Order Imbalances Sorted by Pricing Quantiles

This figure depicts value-weighted buy-sell imbalances of four different order types

sorted by the prices of the securities. For limit orders, observations come from the

TradeSports order book recorded at 30-minute intervals, and value weights are based on

market depth. For market orders, observations come from the TradeSports transaction

archive, and value weights are based on the quantity of securities traded. I sort both

sports and financial securities into five equally-spaced pricing quantiles—(0,20), [20,40),

[40,60), [60,80), and [80,100)—using the securities price from the previous order book

recording or previous transaction. For each of these ten (2x5) groups of securities, I

aggregate each day’s market or limit order buy-sell imbalance. See Table VI and Table

VII for further details.

-20.0%

-15.0%

-10.0%

-5.0%

0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

30.0%

35.0%

1 2 3 4 5

Buy-S

ell

Ord

er I

mbal

ance

in P

erce

nt

Pricing Quantile

Sports Market

Financial Market

Sports Limit

Financial Limit